Algebraic solution for the forward displacement analysis of the general 6-6 stewart mechanism

The anti-control of chaos Newton downhill method finding all real solutions of nonlinear equations was proposed and the forward displacement analysis on the 25th nine-link Barranov truss was completed. Four constrained equations were established by vector method with complex numbers according to four loops of the mechanism and four supplement equations were also established by increasing four variables and the relation of sine and cosine function. The established eight equations are that of forward displacement analysis of the mechanism. Combining Newton downhill method with chaotic sequences, anti-control of chaos Newton downhill method based on utilizing anti-control of chaos in body motion system to obtain locate initial points to find all real solutions of the nonlinear questions was proposed. The numerical example was given.The result shows that all real solutions have been quickly obtained, and it proves the correctness and validity of the proposed method.

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Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

Volume 1A: 25th Biennial Mechanisms Conference ◽

10.1115/detc98/mech-5953 ◽

1998 ◽

Author(s):

Xian-Wen Kong

Keyword(s):

Characteristic Polynomial ◽

Parallel Manipulator ◽

Parallel Manipulators ◽

Dual Solutions ◽

Fourth Degree ◽

Forward Displacement ◽

Displacement Analysis ◽

The Third ◽

Spherical Parallel Manipulator ◽

Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

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Forward displacement analysis of generalized 5SPS-1CCS parallel robot mechanism based on quaternion

Journal of Mechanical Engineering ◽

10.3901/jme.2007.05.008 ◽

2007 ◽

Vol 43 (05) ◽

pp. 8 ◽

Cited By ~ 5

Author(s):

Xiguang HUANG

Keyword(s):

Parallel Robot ◽

Forward Displacement ◽

Displacement Analysis ◽

Forward Displacement Analysis

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Forward Displacement Analysis of a Quadratic Planar Parallel Manipulator: 3-RPR Parallel Manipulator With Similar Triangular Platforms

Volume 2: 32nd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2008-49436 ◽

2008 ◽

Cited By ~ 1

Author(s):

Xianwen Kong ◽

Cle´ment M. Gosselin

Keyword(s):

Unique Solution ◽

Characteristic Polynomial ◽

Parallel Manipulator ◽

Forward Displacement ◽

Displacement Analysis ◽

Planar Parallel Manipulator ◽

Free Region ◽

One To One ◽

Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic parallel manipulator: 3-RPR planar parallel manipulator with similar triangular platforms. Although it has been revealed numerically elsewhere that for this parallel manipulator, the four solutions to the FDA fall, respectively, into its four singularity-free regions (in its workspace), it is unclear if there exists a one-to-one correspondence between the four formulas, each producing one solution to the FDA, and the four singularity-free regions. This paper will prove that such a one-to-one correspondence exists. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified.

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Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator

Volume 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2010-28126 ◽

2010 ◽

Author(s):

Xianwen Kong ◽

Cle´ment Gosselin ◽

James M. Ritchie

Keyword(s):

Parallel Manipulator ◽

Parallel Manipulators ◽

Singularity Analysis ◽

Alternative Formulation ◽

Forward Displacement ◽

Displacement Analysis ◽

Singular Configuration ◽

Actuated Joints ◽

Spherical Parallel Manipulator ◽

Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators — leg actuation singularity — is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.

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Mobility and Position Analysis of a Novel 3-DOF Translational Parallel Mechanism

Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2006-99031 ◽

2006 ◽

Cited By ~ 1

Author(s):

Daxing Zeng ◽

Zhen Huang ◽

Linlin Zhang

Keyword(s):

Closed Form ◽

Parallel Mechanism ◽

Parallel Manipulator ◽

Continuation Method ◽

Mobility Analysis ◽

Forward Displacement ◽

Displacement Analysis ◽

Displacement Problem ◽

Numerical Example ◽

Forward Displacement Analysis

This paper presents the mobility analysis, the inverse and forward displacement analysis, and workspace of a novel 3-DOF 3-RPUR parallel manipulator. Closed-form inverse displacement solutions are obtained by the Denavit-Hartenberg method. The forward displacement problem is analyzed by using the continuation method and proved applying the result of the inverse displacement analysis. The workspace of the mechanism is also obtained. A numerical example is given in the paper.

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Forward Displacement Analysis of a Quadratic Spherical Parallel Manipulator: The Agile Eye

Volume 7: 33rd Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2009-87467 ◽

2009 ◽

Cited By ~ 3

Author(s):

Xianwen Kong ◽

Cle´ment Gosselin

Keyword(s):

Characteristic Polynomial ◽

Parallel Manipulator ◽

Singularity Analysis ◽

Alternative Solution ◽

Alternative Formulation ◽

Forward Displacement ◽

Displacement Analysis ◽

Input Space ◽

Spherical Parallel Manipulator ◽

Forward Displacement Analysis

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic spherical parallel manipulator: the Agile Eye. An alternative formulation of the kinematic equations of the Agile Eye is proposed. The singularity analysis of the Agile Eye is then dealt with. After an alternative solution to the FDA has been presented, a formula is revealed for producing a unique current solution to the FDA for a given set of inputs. A regular cube in the input space, which is singularity free, is also proposed for the Agile Eye. This work will facilitate the control of the Agile Eye.

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